Magnetic integrated double-trap filter utilizing the mutual inductance for reducing current harmonics in high-speed railway traction inverters

Current harmonics are generated at the switching frequency and its multiples when the traction converters are modulated. To address this, multi-trap filters are introduced, which are capable of selectively eliminating these specific harmonics to the limits set by IEEE 519-2014. This targeted removal significantly reduces the need for high total inductance, thereby allowing for a more compact filter design. Comparatively, to traditional inductor-capacitor-inductor (LCL) filters, more magnetic cores are needed for trap inductors. Furthermore, the traction systems have not been examined in conjunction with multi-trap filters. To reduce the filter size and investigate its application in traction converters, this paper presents an integrated double-trap LCL (DTLCL) filter. A tiny capacitor is connected in parallel with the grid-side inductor to form one LC-trap. In addition, another LC-trap is formed by connecting the equivalent trap inductor, introduced through the magnetic coupling between inverter-side and grid-side inductors, in series with the filter capacitor. The presented filters' features are thoroughly analyzed, and the design method has been developed. Finally, the simulation and hardware-in-the-loop (HIL) experiment results validate the proposed method's viability and efficacy. Compared to the discrete windings, the integrated ones enable a size decrease of two cores. Furthermore, the proposed filters can meet IEEE 519-2014 criteria with 0.3% for all the current switching harmonics and total harmonic distortion (THD) of 2.36% of the grid‐side current.

Furthermore, comparing the integrated DTLCL filter to the discrete DTLCL one will be done to verify the effectiveness of magnetic integrated elements in the filter design.
Additionally, the proposed methodology is compared to the SHE technique 46,47 , which utilizes a control system to suppress specific harmonics in the voltage waveform without the need for a resonant trap.However, SHE is limited to offline computations and needs extensive lookup tables at low fundamental frequencies, as well as amplifying higher-order harmonics to eliminate lower-order ones 31,[48][49][50] .In contrast, the proposed technique is relatively easy, capable of achieving similar results at low harmonics, and reduces switching losses while eliminating harmonic distortions and improving output waveforms.It should be noted that while SHE targets voltage harmonics, the proposed approach primarily addresses current harmonics, which indirectly enhances voltage waveform quality due to the intrinsic relationship between current and voltage in electrical systems.Furthermore, the LCL filter capacitor and the inductance generated by the coupling effect between the two inductors create a trap without the need for additional elements, and the utilization of one magnetic core for both inductors results in a smaller overall size and associated cost savings.
The contributions of this paper are listed below: 1.An integrated double-trap filter is designed, simulated, and validated.2. A detailed analysis of the many inductors for magnetic integration has been presented.3. The performance of the harmonics removal and size reduction has been utilized to validate the proposed methodology.4. The application, which is, in this case, railway traction converters, can be extended to other grid-connected inverters/rectifiers, including industrial power systems, renewable energy systems, and building power systems.5. Identification of the potential to integrate the DTLCL filter directly into transformers, suggesting a promising direction for future research to enhance system integration and efficiency.
In this paper, following the introduction, the basic theory and operation characteristics of the proposed integrated DTLCL filter are introduced in "System structure and magnetic circuit analysis"."Designing and modeling of magnetic integrated DTLCL filter" presents the magnetic integration approach, then the optimal design method to reduce filter inductances is proposed.Simulation and HIL experimental results to verify the feasibility and effectiveness of the proposed design are described in "Simulation and HIL experimental validation".Lastly, "Conclusion" concludes the paper.

System structure
The standard TPSS arrangement utilized in China's HSR is shown in Fig. 1 8 .To provide the all-parallel autotransformer (AT)-fed network, the three-phase 220 kV network voltage is stepped down to 27.5 kV single-phase double-feeders within the power supply station.TTs could be connected using single-phase, V/v(V/x), Ynd11, and Scott, among other methods.The V/x-structure TT is used by Chinese and German HSR due to its excellent capacity utilization, easy wiring, and compliance with AT catenary systems 1 .The all-parallel AT-fed TPSS scheme is commonly used in HSR and massive trains throughout the world due to its advantages of extended power supply, minimal voltage drop, and electromagnetic compatibility 32 .The ATs, mounted at the AT substation or section post, are separated along the track by roughly 10 to 15 km.In the complex AT traction electricity network, the feeders, contact lines, protection lines, communications cables, rail, and integrated grounding cables are all considered multiconductor transmission lines.Figure 1 depicts an equivalent single-phase inverter driving setup for HST.The line-side converter at every HST's electric grid is made up of two PWM converters connected in parallel.Two interleaved single-phase two-level rectifiers are used in the power conversion step in Fig. 1 to reach a good current carrying capacity and power factor.As shown in 1 , the train converter is frequently two-level, several interlaced, two-or three-level.The whole paper uses two interleaved two-level PWM inverters and grid configurations of an all-parallel AT-fed EMU drive unit for analysis.There are, however, several other grid configurations and EMU kinds, as was already indicated.However, the results of the simulation and HIL experiments and the established rule of the researched filter apply to those other configurations, which opens up the possibility of multiple distinct lines of future study.
As this paper mainly focuses on the application of the magnetic integrated DTLCL filter, the detailed mathematical model of HSR and initial parameters are not shown here, which has previously been explored in research in 1,2,5,8,[51][52][53] .For example, using the nodal admittance matrix, a uniform mathematical model of TPSS and China HST is presented in 51 .The HSR modeling can potentially affect the filtering effect of the integrated DTLCL filter.The modeling of the HSR system, including the power converters, power cables, and load, can affect the performance of the integrated DTLCL filter in several ways.For example, the impedance of the load and the power cables can influence the filter's resonant frequency, affecting its ability to attenuate harmonics.
Additionally, the type and level of nonlinearities presented in the HSR system can affect the harmonic content of the signals transmitted through the filter, which can also impact its performance.As described in Fig. 1, the integrated DTLCL filter is placed in the PWM-controlled train to suppress the harmonic generated by the traction converter since it is the origin of harmonics in the low voltage side of the TT.Therefore, the traction grid is seen from the filter as a typical linear element, with v gg representing the contact-line voltage in the train location, while the equivalent load is seen as a fixed resistance 2,8,11,53 .Thus, to simplify the analysis, the values of the EMUs' converter parameters affecting the filter design and performance are listed in "Designing and modeling of magnetic integrated DTLCL filter".The different grid modeling affects the designed parameters and filtering effect of the integrated DTLCL filter.However, the design concept and work principle are the same.This analysis is also applicable to the other passive filters.
The harmonics assessment circuit illustration from the line-side traction converter to the traction electrical network is shown in Fig. 2. It is filtered by an integrated DTLCL filter.Here, a single integrated DTLCL converter is used to represent a typical single H-bridge configuration for analysis's sake.This approach is justified by the similarity and equivalent configuration of the two H-bridges in the system, allowing accurately predicting the harmonics reduction potential of the DTLCL filter in traction converters.Moreover, this research focuses on assessing the effectiveness of the magnetic integration of the DTLCL filter specifically in traction converter applications.Thus, by modeling only one of the similar H-bridges, it is aimed to streamline the analysis while ensuring that the findings are representative and applicable to both bridges given their equivalency.With a transformation ratio of 27.5/1.55,the TT may be regarded as a standard linear unit.The equivalent leakage inductor of the secondary side of the TT is represented by L s as well.It needs to be noticed that this exact setup does not significantly limit the installation of trap filters.These filters may often be used in dc/ac or ac/dc generation systems, single-or three-phase, and standalone or grid-connected 36 .In this case, C dc stands for the dc-link capacitor, R dc for the equivalent load of a single integrated DTLCL-type rectifier on the traction inverter-motor drive system, and I Rdc and I Cdc for their currents.Four switches designated as S1-S4 that operate at f sw transform the dc-link voltage V dc into ac voltage v in that contains harmonics at the dominating switching frequency 2f sw and its multiples 54 .The harmonics are concentrated around 2f sw when using a unipolar sinusoidal PWM (SPWM).Thus, 2f sw is the actual switching frequency.It is also important to remember that harmonics at the double and fourfold switching frequencies 2f sw and 4f sw are much more prominent than those at high switching frequencies, which have the most output current harmonics.For this reason, the total harmonics can be effectively decreased by eliminating the harmonics at 2f sw and 4f sw .In real situations, two LC-traps are favoured due to their lower expense and size, and this is the approach that is further investigated in this work.The TT might be viewed as a typical transformer.For creating the worst instability situation, the equivalent series resistors of the filter components are disregarded.
The inverter-side and grid-side inductors, L i and L g , are connected in series.The voltages of the two inductors are v i and v g , respectively.Additionally, i il and i gl are the currents flowing through the two inductors.Moreover, i gc denotes the currents flowing through the capacitors C g .At the same time, the inverter-side current, the grid-side current, and the dc bus current are represented by i i , i g , and I dc , respectively.A shunt filter capacitor C f has been inserted at the connection point of L i and L g .The voltage at this point is denoted by v f , whereas i f represents the The filtration effectiveness of the passive filters can be considerably impacted by the traction grid conditions.The traction grid is assumed to be weak in this article's analysis, which means that the short circuit ratio is significantly low.As a result, the grid impedance may dramatically vary 55 .For the worst case of instability, the grid might be described as a typical voltage source with series grid inductance.Since the grid resistance would reduce the resonant peaks, the focus will only be on the impact of the grid inductance, denoted by L s in Fig. 2.Moreover, when many converters operate simultaneously to share power, the corresponding grid inductance detected by one converter might be proportional to the number of converters.The impact of the grid impedance gets bigger when the number of converters rises 35 .According to 43 , increased L s could weaken the resonance poles.It has been discovered as a result that the filter experiences minor transient variations before going back to its setpoint.Despite this, the system's dynamic reaction required a longer time compared to the stiff grid circumstances.This paper focuses primarily on the application of the magnetic integrated DTLCL filter, and thus does not consider the use of L s as the filter inductor of the H-bridge for estimating size reduction.This aspect has been extensively covered in previous studies, such as 11,32,56,57 , which detail the integration of filtering inductors in traction transformers for harmonic suppression.Additionally, the independence of the proposed DTLCL filter from L s aligns with its broader applicability across various power electronics-based systems.This includes scenarios in strong grid conditions where no significant inductance is present, underscoring the versatility and robustness of the filter in diverse operational environments.

Proposed magnetic integration approach of DTLCL Filter
This section will explore a detailed methodology for designing the presented magnetic integration approach of a DTLCL filter.The design concept of the passive filter inductors was discussed in detail throughout the relevant literature.In typical LCL filters, the grid-side and inverter-side inductors each have their dedicated inductor, which requires the fabrication of two inductors.Suppose two LC-traps are used for the SPRLCL filter 9 , i.e., the equivalent discrete filter to the integrated DTLCL one and the discrete DTLCL filter, as shown in "Integrated DTLCL filter's properties and filtering effectiveness".In that case, it is necessary to fabricate one extra inductor and one extra capacitor in addition to the grid-side and inverter-side inductors.Thus, the discrete SPRLCL or DTLCL filter still suffers from large size and expense because of the need for one capacitor and one magnetic core for the trap inductor.This is the case even if the overall inductance is lower than typical LCL filters.Magnetic integration, which is an excellent technique that has previously been used in LCL 40,41 and LLCL 42,43 filters, is recommended for more improvement of the power density while saving expenses.
Using the LLCL filters' magnetic integration as a basis, Fig. 3a illustrates the magnetic integration for the DTLCL filter, where to avoid magnetic saturation, two air gaps are introduced in the side limbs, and one air gap is also put in the central limb of a closed magnetic circuit made up of two E-type magnetic cores.Additionally, the central limb's cross-section area is double that of the side limbs to prevent magnetic saturation.In reality, E-type cores with these sizes have often been produced for industrial purposes.The main parameters for building the filter inductor are, in general, the size and material of the magnetic core, the number of turns N i and N g , and the lengths of the central and side limbs air gaps l gc and l gs .Air gaps can be included to prevent magnetic saturation, although doing so reduces the magnetic permeability effectiveness, necessitating a large number of turns to produce the appropriate inductances.The magnetic circuit model is shown in Fig. 3b, but the reluctances of the yokes and limbs of the magnetic core are ignored since, in the magnetic circuit, the air-gap reluctances are so much bigger than the other ones.R i , R m , and R g , i.e., the magnetic resistance of the three limbs, may therefore be expressed more simply as functions of the air-gap reluctances.It is necessary to assess the flux density to design the magnetic core of the integrated filter inductors.Figure 4 depicts the electric connection schematic for such a circuit.By winding L i and L g on the side limbs with N i and N g , the coupling influence may be fully used to lower the filter size.In such a magnetic core, the L i and L g windings are negatively coupled because the flux directions at the side limbs are opposite.The central concept of the presented magnetic integration is constructing a trapinductor via the magnetic coupling between L i and L g inductors called an active trap inductor.
In contrast, the other trap is formed by connecting a shunt capacitor C g with L g winding.In the proposed design, integrating L i and L g introduces a coupling inductor for one of the two LC traps.Based on Fig. 3b, Φ  to the flux generated by L i winding.In contrast, Φ im and Φ ig are the fluxes generated by L i winding and flowing across the central limb and L g winding, respectively, as described in Eq. ( 1), where the magnetic resistors of the three limbs can be referred to by R i , R m , and R g , respectively 35,36,43,44 .
L g winding also generates the flux Φ g , where the fluxes generated by L g and flowing across the central limb and L i winding are Φ gm and Φ gi , respectively, as described in Eq. ( 2) 35,36,43,44 .
Every inductor winding's total flux consists of the self-flux and the mutual flux.Then, Eq. ( 3) might be used to define V i and V g 43,44 .Moreover, they can be described, according to Eqs. ( 1)-( 3), as in Eq. ( 4) 36,43 , where the self-inductances L i and L g and the mutual inductances M ig and M gi could be described as in Eq. ( 5) 35,36,42,43 .
As a note, M ig and M gi are identical, and both could be written as M ig .It is apparent that the two inductors are coupling according to Eqs. ( 4) and ( 5), and the following could represent V i and V g 42,43 .
(1) Based on Eq. ( 5), the self and mutual inductances are determined by the magnetic resistances that could be defined by Eq. (7).In this equation, l gs and l gc denote the side and central limbs' air gap lengths, and A S and A C represent the side and central limbs' cross-section areas, with A S = 1/2A C .Moreover, μ 0 = 4π × 10 −7 N/A 2 refers to the air permeability 35,36,[42][43][44] .In the end, the self and mutual inductances are determined with Eq. ( 8) by putting Eq. ( 7) in Eq. ( 5) 35,36,43 .As illustrated in Eq. ( 9), the coupling coefficient k Mig is a metric that quantifies the degree of mutual inductance between two coupled circuits represented as the ratio of the mutual inductance to the square root of the product of the self-inductances.Furthermore, it can be found that the coupling coefficient could be effectively tuned by varying the air gap lengths l gc and l gs , or their ratio l gc /l gs .
The proposed approach can accomplish the formation of one equivalent trap inductor by using the magnetic coupling between two windings, as seen in "Integrated DTLCL filter's properties and filtering effectiveness".Consequently, it is possible to avoid needing two magnetic cores and decrease the expense and size of the DTLCL filter.Furthermore, it is observed that, in contrast to the discrete SPRLCL filter, there is no extra component.

Integrated DTLCL filter's properties and filtering effectiveness
Figure 4 depicts the circuit structure of the integrated DTLCL filter, consisting of an inverter-side inductance L i , in addition to two LC traps.These two LC-traps (one is M ig -C f and the other is L g -C g ) are resonated to the dominant switching frequency 2f sw and its first multiple 4f sw because the harmonics are concentrated around 2f sw when using a unipolar sinusoidal PWM (SPWM), where, 2f sw is the actual switching frequency.The mutual inductor M ig is used in the integrated DTLCL filter for building a resonant trap with C f .In contrast, L g is used for creating another resonant trap with C g for attenuating the switching harmonics.The resonance tanks eliminate the specific harmonics of the output current.At the same time, the other harmonics are attenuated by the whole filter.This paper proposes a method to design the integrated DTLCL filter by tuning the series resonant frequency to 2f sw and the parallel resonant frequency to 4f sw .
Moreover, the block diagram of the proposed filter is presented in Fig. 5.The transfer function G DTLCL (s) of the integrated DTLCL filter, from v in to i g , is calculated in Eq. (10), where the coefficients can be found in the Suppl.Appendix.
The magnetic coupling is a key factor that has a great influence on the performance of the filter.According to Eq. ( 10), the mutual inductance is critical in calculating the transfer function for the overall system and, consequently, the frequency of the resonances and traps.By adjusting the mutual inductances, in other words, by tuning the coupling coefficients, these frequencies are effectively adjusted.Moreover, Eq. ( 9) demonstrates that the coupling coefficient may be effectively adjusted by changing the ratio l gs /l gc .Therefore, this ratio affects the transfer function of the whole plant, where this ratio is changed from around zero, i.e., l gs ≈ 0, to about infinity, i.e., l gc = 0.According to Eq. ( 8), it should be noted that l gs cannot be zero, but it can just be very little relative ( 7) to l gc , while l gc can be zero.It can be stated that k Mig values are inversely proportional to the l gs /l gc values.These values are changed from around one to about zero.
From Eq. ( 10), it can be found that G DTLCL (s) has two zeros at ω t1 = (1/(C f M ig )) 1/2 and ω t2 = (1/(C g L g )) 1/2 , respectively, where ω t1 and ω t2 represent the trap angular frequencies.The corresponding switching harmonics may be efficiently suppressed by setting those two frequencies to the dominant switching frequency, as indicated in Eqs.(11) and (12).Moreover, the effectiveness of the proposed integrated DTLCL filter in reducing total harmonic distortion (THD) will be substantiated through simulation and HIL experimentation, as outlined in "Simulation and HIL experimental validation".
The Bode diagrams i g (s)/v in (s) of the integrated DTLCL and discrete SPRLCL, LCL, and L filters are shown in Fig. 6 using the parameters depicted in Table 1.Section 3.1 goes into more depth about the steps taken to design these parameters.As Fig. 6 shows, the integrated DTLCL filter keeps the discrete SPRLCL filter's features and makes a strong harmonics suppression at 2f sw and 4f sw , where those two frequencies have two magnitude traps.
Furthermore, Fig. 6 shows that the magnitude-frequency characteristics of G DTLCL (s) have two conjugate resonant peaks because the degree of their denominator is 5.These resonant peaks are obtained by putting the denominator of G DTLCL (s) in Eq. ( 10) equals zero, substituting s with jω.The first resonFant frequency of the magnetic integrated DTLCL filter can be approximated as in Eq. ( 13) 42,43 , where ω res1 represents the resonant angular frequency and f res1 represents the resonant frequency.
As Fig. 6 shows, although the discrete LCL filter has the largest roll-off rate of −60 dB/dec at the highfrequency domains, it has no trap magnitude, which weakens its suppression in the switching frequencies.It is essential to design the second resonant frequency far off the switching frequency multiples to prevent the harmonics amplification 26,35 and located around 2.5 kHz, as seen in Fig. 6 .After the second resonant frequency, the proposed integrated DTLCL filter has a harmonics suppression of −20 dB/dec.(11)    The resonant peaks may cause system stability problems.Several damping approaches, including passive damping 21,22,58 , and active damping [59][60][61][62][63] , have been proposed to ensure system stability.Designing the resonant frequency beyond the Nyquist frequency is adopted because of the additional losses of passive dampening techniques and the great sensor expenses of active dampening techniques 43,64 .In addition, the parasitic filter resistances may offer excellent dampening for enhancing system stability and performance.Other works have previously done extensive stability analysis 43,64 .Therefore, it is not included here since this chapter emphasizes the magnetic integration of the DTLCL filter.

Designing and modeling of magnetic integrated DTLCL filter
This part of the paper will explore a detailed methodology to design the DTLCL filter's parameters.The ac grid is assumed to be weak in the design process in this paper, with a grid inductance of L s = 4 mH.This inductance value, along with other parameter values for the EMUs inverter listed in Table 2, is derived, with slight modifications, from empirical data used in references 45,53,65 .These references report the usage of similar or even higher values of L s in comparable applications, specifically under conditions where a high series grid inductance is indispensable due to grid instability.The choice of L s , although appearing elevated for general applications, is meticulously selected to align with the realistic operational scenarios our study addresses and is substantiated by literature that investigates similar conditions of grid dynamics.The magnetic integrated DTLCL filter parameters might be designed by implementing the system parameters listed in Table 2 in light of the regulations of the harmonic suppression meets IEEE 519-2014 8,66,67 , the consumed reactive power under 5%, and the inverter-side current ripple ΔI Li less than 40%.Based on R dc , the inverter functions as a rectifier here.Moreover, designing L i , which is based on the LCL filter's design method in 8 , is the first step in the design process of the magnetic integrated DTLCL filter.As a result, L i is designed as in ( 14) for a single-phase H-bridge unipolar SPWM inverter with ΔI Li ≤ 40%, considering protecting the IGBTs and preventing saturation of the inverter-side inductor.Because such a system can reach the lowest possible resonance frequency to accomplish the maximum amount of inductor utilization, the L g design is equivalent to the L i design 37,38,64,68 .However, because the maximum current and ripple current have decreased by around 40%, L g has been decreased to 1.3 mH.
To maintain the ac voltage drop in the inductors to less than 10% of the root-mean-square (RMS) value of v gg , the total inductance L total = L i + L g must be monitored 9 .
When selecting the capacitor C f , the reactive power drawn at the fundamental frequency and harmonics elimination at high frequencies should be justified 8,69 .C f may reach a small value like 125 µF while taking into account the permitted reactive power.
In addition, M ig is designed by satisfying Eqs. ( 11) and ( 13), i.e., f r1 of the magnetic integrated DTLCL filter is between 1/2f sw and 5/6f sw , while f t1 equals 2f sw , i.e., f t1 = 1.1 kHz.To improve stability and attenuate the reduction of inductance with increasing current, f r1 = 2/3f sw = 367 Hz was used as a midpoint value 43,64 .Consequently, M ig has been calculated as 0.167 mH.
Moreover, based on Eq. ( 9), the relevant coupling coefficient k Mig is designed as 0.115 to adjust the second resonant frequency above 4f sw .As a result, l gs /l gc can be calculated to be 3.85, which proves that l gs determines L i and L g .
The additional capacitor C g is determined by Eq. ( 12), which can be derived as 4.619 µF.Nevertheless, to meet the power factor criterion, the total capacitance C total = C f + C g must be constrained by the amount of reactive power consumed under the rated circumstances.furthermore, if C total exceeded 0.05 p.u, the reactive current would be high 8,64 .The increase in filter inductance could help to solve this problem.Furthermore, Fig. 7 displays the elaborate design flowchart for the presented integrated DTLCL filter.This figure illustrates the flowchart of the design method as a general case, in which if one of the conditions is not fulfilled, the design process goes back to the first step.As for the inductance presented in Eq. ( 14) and other parameter values, they are presented as a design example to show the proposed filter design validity.In addition, according to the verification results, all the conditions are satisfied.Therefore, there is no need to go back to the first step of the design process.Furthermore, the designed parameters are slightly adjusted, and the presented ones are the final version.
In addition, the integrated inductors' power loss is minimized by using Litz wires with small ESRs and 0.5π mm 2 cross-section area (S ω ).The subsequent steps outline the design criteria for the suggested magnetic integration approach using the previously designed inductances.Choosing an EE-type magnetic core, along with its size ( 14) www.nature.com/scientificreports/and material, comes first.The saturation flux density B sat , relative permeability μ r , resistivity, and cost are typically considered when choosing a magnetic material.Higher B sat or μ r can reduce the number of turns of the inductor, which reduces the size and weight.In contrast, the eddy current losses can be lowered by higher resistivity.The magnetic material is chosen to compromise price, efficiency, size, and weight to get a cost-effective inductor.The well-known area-product approach 70 may be used to choose the magnetic core's dimensions.The area-product (A P ) of the cross-section and window areas (A S and A W ) of L i is used to choose the magnetic core for the integrated windings.The EE magnetic cores are chosen depending on this technique 70 with L i = 1.63 mH, inductor's maximum current I il-max = 800 A, and maximum flux density of magnetic core B max = 0.35 T, where B max is set as λB sat with 0 < λ < 1, and B sat is 0.49 T at 25 °C.λ is designed at 0.714 to guarantee a reasonable margin (30%).
Based on the NCD products catalog 71 , a pair of E 320/160/40 cores could be chosen, with A S = 1.66 × 10 -3 m 2 and A W = 18.84 × 10 -3 m 2 , resulting in an area-product of 31.27 × 10 -6 m 4 ≈ 2A P , which leaves a large margin of size.
The SPRLCL filter would be designed by following the same procedure, implying that L i , L g , and C f equal those of the integrated DTLCL one for providing a reasonable assessment.The additional inductor L f is determined by Eq. ( 11), replacing M ig with L f , which is designed to be 0.167 mH.The additional capacitor C g is determined by Eq. ( 12), with M ig = 0, which can be derived as 4.026 µF.
Using a similar technique, the LCL filter is designed, where L i , L g , and C f must be comparable to those of the proposed filter to offer a reliable evaluation.
Similarly, the L filter is set to match the L total of the proposed filter because of the same purposes or equal the LCL filter by setting C f = 0 μF.
After completing the design processes, all of the integrated DTLCL, discrete SPRLCL, LCL, and L filter parameters are provided in Table 1.In addition, the same controller implemented in 36,43,45,48,53,65,72  As noted, the proposed integrated double-trap filter can produce the equivalent additional inductor, thus saving one inductor with its components.In addition, the proposed magnetic integration can also save one magnetic core.This is because L i and L g could be wound on the side limbs of one magnetic core instead of three magnetic cores like the discrete SPRLCL filter and other types like LTCL and LCL-LC filters.
The comparison between the sizes of integrated inductors and discrete ones is essential.The discrete inductors of the SPRLCL filter could be, respectively, coiled on the middle limbs of three cores.The filter inductances of the integrated DTLCL filter and the SPRLCL one are configured to be similar to ensure adequate comparison.The discrete SPRLCL filter has the most considerable size with three cores.In contrast, the discrete LCL filter has two cores, while the integrated DTLCL and discrete L filters have one core each.

Simulation and HIL experimental validation
To evaluate the performance of the proposed filter and design method, simulations using MATLAB/Simulink and HIL experiments were carried out on a traction inverter.The proposed filter could be validated by its comparison with the discrete SPRLCL, LCL, and L filters.The system's basic parameters used in the simulation and HIL experiments are described in Tables 1 and 2. With these parameters, verification models were constructed based on the system configurations shown in Fig. 2.
Analyses of the strengths and weaknesses, endurance, complexity, and size of several passive filters are conducted.The ability to attenuate harmonics and the transient performance of four filters are therefore examined using simulations and HIL testing.The several performance indexes that have been computed are listed in Table 3.

Simulation results
Figure 8a shows the simulated steady-state waveforms of i g , i i , v gg , and V dc with the proposed integrated DTLCL filter.As can be seen, V dc here approximates 3000 V, and the error is only 150 V (5%) owing to the control system's voltage loop.Furthermore, i g is well filtered in the steady state to be hugely sinusoidal.Figure 8b shows that its THD is just 2.36%, which is very low.A significant reason for this is the proposed DTLCL filter's ability to attenuate low-order harmonics and the double and fourfold switching-frequency harmonics to a combined attenuation of 0.01% and 0.00%, respectively.The harmonic currents on the grid-side inductor beyond 4f sw are also eliminated well, with sixfold switching-frequency harmonics of 0.04% of the fundamental current.From Fig. 8b, it is evident that there is a harmonic spike around 2.5 kHz that corresponds to the second resonance peak, confirming the theoretical analysis and Bode diagrams depicted in Fig. 6.In this case, all the harmonic currents can be limited to less than the limit of 0.3%, which complies with IEEE 519-2014 criteria.The switching harmonics composition is shown in Table 3.
Figure 9a illustrates the simulated waveforms of the traction inverter employing the discrete SPRLCL filter for comparative purposes.This part compares the performance of the proposed integrated filter and its discrete counterpart.Therefore, the same test has also been conducted for the discrete SPRLCL filter, as shown in Figs. 8  and 9.The waveform of i g retains sinusoidal when the integrated DTLCL filter is substituted with the discrete SPRLCL filter, demonstrating that the harmonics compensating at low frequencies would not be impacted.Furthermore, as illustrated in Fig. 9b, the 2f sw and 4f sw harmonics of i g are much reduced.The harmonics of i g over the fourfold switching frequency are also efficiently suppressed.The sixfold switching-frequency harmonics are 0.04% of the fundamental component, much lower than the limits.Here, it is also apparent that there is a harmonic spike around 2.5 kHz, which confirms the theoretical analysis and Bode diagrams shown in Fig. 6.Table 3 shows that the specified SPRLCL filter can meet IEEE criteria with a grid-side current THD of 2.12% but with bigger filter components.As demonstrated, the suggested filter, in general, performs similarly to the discrete SPRLCL filter, implying its effectiveness with a small size.
Figure 10 shows the simulated results of the traction inverter filtered by the conventional LCL filter.The waveforms are shown in Fig. 10a, while the spectra of i g and i i are shown in Fig. 10b.As depicted in Fig. 10b, the third harmonic of i g exceeds the threshold of 4.00% of the fundamental component.This unipolar modulated traction inverter's somewhat inadequate performance can be attributed to its relatively low switching frequency and modest filter inductors.THD of i g is 4.34%, less than the permissible level.However, the discrete LCL filter requires two magnetic cores compared to one for the proposed filter.The simulated results of the traction inverter with an L filter are shown in Fig. 11a.Only the simulated waveform of i g is shown since the waveform of i i is identical.This is due to the L filter being a series inductance; thus, i i and i g are essentially the same, making it redundant to plot both current waveforms.Although i g is filtered to a sinusoidal signal and in phase with v gg , a current spiking at the 39 th harmonic, near 4f sw , is observed, as illustrated in Fig. 11b.This occurrence is due to the L filter's limited ability to attenuate high-frequency harmonics, specifically at the dominant switching frequencies such as 2f sw and 4f sw , where the absence of a parallel LC-trap allows these harmonics to pass through the converter branch loop, which confirms the theoretical analysis and Bode diagrams shown in Fig. 6.As per IEEE Standard 519-2014, harmonics beyond the 35 th order should be reduced to less than 0.3% of the nominal fundamental current.However, the 39th harmonic reaches approximately 0.4%, thus exceeding this limit and contributing to the non-compliance with grid regulations.The grid regulations are then broken.Moreover, V dc will decrease to around 2560 V, leading to inadequate inverter operation and perhaps traction stoppage.A V dc of 2560 V is not permitted in reality.Hence, additional investigation into this subject is recommended.
Although this paper primarily focuses on the THDi and its implications for current harmonics, the voltage waveforms v gg and V dc are included to provide a comprehensive view of the system behavior under different filtering conditions.The intrinsic relationship between current and voltage in electrical systems dictates that changes in current harmonics directly affect voltage quality.Given the critical role of voltage stability in traction inverter systems, which affects operational efficacy and system reliability, maintaining voltage waveform integrity is crucial.The observed decrease in V dc , which can lead to traction stoppage, underscores the importance of these waveforms in the presented analysis in this paper.
From Table 3, although the THDs of the four filters, except the L one, are satisfied at less than 5%, the required inductance of the output filter differs.Moreover, the current switching harmonics of the first two filters at the LC-trap frequencies are nearly identical, proving the proposed approaches' validity.Furthermore, there are two magnetic cores saved compared to the discrete SPRLCL filter and one magnetic core in comparison with the discrete LCL one.Hence, the proposed filter reduces expenses and size.Although the integrated DTLCL filter is smaller and lighter compared to the discrete SPRLCL and LCL ones, a thorough assessment must take the inductors' power loss into account.Because it is unstable, the L filter is not taken into consideration herein.The detailed analysis of the inductors' power losses, which has previously been explored in previous research 43 , is not included here since the primary focus of this paper is on the magnetic integration and application of the DTLCL filter in traction inverters.Inductors often lose power as a result of core and winding copper losses.Due to the numerous harmonics in i i and v i , the power loss of the inductors could not be computed or measured directly.To accurately evaluate the inductors' power loss of the integrated DTLCL, discrete SPRLCL, and LCL ones, the system efficiency is determined under similar circumstances.When performing under a unit factor, P in denotes the input active power calculated using P in = V gg I grms , while P o denotes the output active power calculated using P o = V dc I dc .The efficiency of the system is assessed using the ratio P o /P in .The average values of i dc and v dc that can be calculated or measured directly are I dc and V dc .I grms and V gg are the RMS values of i g and v gg .The power loss is calculated by subtracting P o from P in .The system efficiency of the integrated DTLCL and discrete SPRLCL and LCL ones under conditions equivalent to full load are 97.52%,97.44%, and 97.37%, respectively.The efficiency is roughly equal to 97.3%, indicating low system power losses.
The load variation testing is performed on the proposed integrated DTLCL filter, where the related simulated waveforms are displayed in Fig. 12.At t = 0.8 s, the load was increased to 125% of its rated value (10 → 12.5 Ω).The capability of the filter to suppress instability, which is determined by going back to the setpoint, is the most crucial requirement in the transient state.As can be seen, the integrated DTLCL filter is strong enough to maintain stability even though the load varied by 25% in the transient duration.The dc-link voltage spike is lower than 300 V, and the total variation length was 0.12 s, followed by a smooth return to the setpoint, indicating a well-designed filter.
A 300 V step-down variation in V dc (3000 → 2700 V) was performed at t = 0.8 s using the proposed integrated DTLCL filter to check the dynamic operation, where Fig. 13 shows the simulated waveforms.It is shown that before returning to the setpoint without fluctuating, the filter experiences a few transients.The system's dynamic responsiveness required a brief time until the current started following its reference, even though the transient phase lasted only for around 80 ms.As can be seen, the stability was preserved by the integrated DTLCL filter.Moreover, the proposed approach still demonstrates strong switching harmonics suppression abilities during the dynamic phase.Figures 12 and 13 show that the grid-side current is almost ringing-free.On the other hand, the system's dynamic responsiveness requests more time until the current follows the reference, leading to a longer dynamic period.According to the simulated results, because the integrated DTLCL filter has a sturdy construction, it is acceptable for traction networks.

HIL experimental results
For further verification, the experiments are also conducted on the HIL platform.The HIL experiments platform is set up to validate and test the presented filters' superiority, durability, and stability.The main advantage of the HIL experimental platform is that the real prototype may be evaluated without the need for underlying devices, as shown in Fig. 14 73 .Another advantage is that the designer need not depend on environmental or natural testing.Additionally, because the models could depict the plants, it is useful and economical.Using HIL, it is feasible to reduce the expense of physical validations in addition to the effort and time required for developing modifications in a wide range of situations 74,75 .Moreover, HIL experiments ease the recognition and redesigning barriers.In addition, it enables the real-time test to progress through the entire process more quickly than the physical test.Furthermore, HIL is preferable to physical tests in precision and expense since it can be designed and operated on a timetable.
This method has shown considerable potential for business and academics thanks to HIL's ability to provide risk-free equipment and a speedy prototyping approach in research and engineering 4,8,32,36,43,53,[72][73][74][75][76][77][78][79][80][81] .In cases when an extensive system is employed, HIL experiments may offer a secure testing environment.HIL is an attractive technique that offers the capabilities to test design methodology in a scenario of extensive systems with many complicated independent models that have high switching frequencies or quick dynamic behavior 4,8,32,53,74,76,81 .Furthermore, HIL is a contemporary technique frequently utilized for power electronic system testing and validation.To address the problems of difficulties, complexities, and expense, HIL has been used to assess power www.nature.com/scientificreports/inverters 73,75,[77][78][79][80] .The evaluation by HIL validation of the network-tied converter with passive filters is made more desirable, according to the results in 8,32,36,43,72,77,78 .
The presented filter is currently in the research phase, which must be clarified.Rather than the physical filter design that could happen in the subsequent phases, the presented filters would be created and evaluated utilizing the HIL platform during this phase since this is more cost-efficient and it is impossible to build an actual TPSS at laboratory tests.It is essential to note that the HIL technique is a powerful validation tool for new design techniques in large systems like TPSS since, with its help, it is possible to assess the accuracy and efficiency of the investigated systems without having to spend funds for their real implementation 4,8,32,53,74,76,81 .The standard method in the HIL technique is used in this study to represent the presented filters.Utilizing this standard method for the examined circuit, it is believed that the HIL technique offers relevant results that are extremely near to those of the real tests, as in the systems presented in 8,32,36,43,72,77,78 .
A fast control prototyping unit developed by StarSim modeling and integrated into the NI PXle-8821-FPGA-7868R real-time controller (RTC) and the NI PXle-8821-7846R real-time simulator (RTS) are all part of the HIL 76 , as shown in Fig. 15.The HIL also includes a power system emulating unit, hardware input/output ports, an oscilloscope, and a host computer.The translucent backboard of the NI PXle-1082 has eight slots and offers exceptional performance and output power.Moreover, HIL matches the OXI-5 PXI hardware requirements, www.nature.com/scientificreports/has improved synchronization features, and delivers a high degree of reliability, leading to a low mean time for repairing 75 .MATLAB/Simulink can be utilized for programming the control system, where the fixed-step solver can be used.Using the modeling program StarSim, the grid-connected rectifier with filter and control system models is uploaded into the HIL.Executing the grid-connected rectifier with filter model and control system model in RTS and RTC, respectively, results in constructing a closed loop.Like the simulation verification, identical parameters are used.The oscilloscope and monitor could be used for tracking the voltage and current waveforms.The oscilloscope may also provide data for the experimental current/voltage waveforms, which might then be uploaded to the MATLAB/Simulink program and examined with the Powergui FFT Analysis Tool.
Figure 16 depicts the experimental waveforms with the harmonic spectrum of i g of the integrated DTLCL filter.The controller causes V dc to be close to 3000 V, and the error is only 150 V (5%).Additionally, i g is appropriately filtered to be extremely sinusoidal.Because of placing the two LC-traps at the frequencies of 1.1 and 2. the current switching harmonics were significantly decreased below 0.3% of the rated current, and the system meets the IEEE 519-2014 regulations.
For comparison, Fig. 17 shows the experimental results obtained using a discrete SPRLCL filter as a substitute for the proposed integrated DTLCL filter.The i g waveform maintains its sinusoidal shape, proving that the loworder harmonics compensation is unaffected.The double and four-fold switching frequency harmonics, which are the two prominent current switching harmonics, have been effectively diminished.Compared with Fig. 16, the performance of the proposed filter is often comparable to that of the discrete SPRLCL one, indicating that it is effective despite being small in size.
Figure 18 illustrates the experimental waveforms and i g harmonic spectrum of the discrete LCL filter.The low-order harmonics of i g were found to nearly surpass the limits.This problem is caused by the low switching frequency of the unipolar modulated traction inverter and tiny filter inductors.Like the simulated results in Fig. 10, the THD of i g was seen as less than allowable levels.
Figure 19 depicts the experimental results of the conventional L filter.Although i g is filtered to a sinusoidal shape and in phase with v gg , a current spiking in the 39 th harmonic, beside 4f sw , was observed, which is a breach   of the network regulation.Furthermore, the V dc decreased to around 2560 V, like the simulated results in Fig. 11.Consequently, this situation may lead to bad inverter performance or traction blocking.A 2560 V V dc must not be allowed.As a result, additional research needs to look at the problem more thoroughly.
A step variation in the dc load occurred to investigate the system's transient performance of the integrated DTLCL filter.Figure 20 depicts the experimental results when the load gets a step change from 10 to 12.5 Ω at 0.8 s to evaluate the proposed filter's capacity to follow commands.As shown, the system can function appropriately in the face of transient occurrences, comparable to the simulation results in Fig. 12.The essential need in the transient state is the filter's capacity to suppress instability, which is assessed by returning to the setpoint.The integrated DTLCL filter is powerful enough to ensure stability even when the load varies.As observed, the dc-link voltage experienced a voltage rise before progressively dropping to the setpoint.
Next, the dynamic test was performed for the DTLCL filter, where Fig. 21 shows the experimental results of a 300 V step-down variation in the dc-link voltage.As can be observed, the waveforms are comparable to those simulated in Fig. 13, proving that the filter can provide both stability and switching harmonic attenuation.The DTLCL filter is seen to have certain transient moments and then return to its setpoint with no fluctuation, which verifies the system's robustness.Even though the transient phase only lasted for around 80 ms, the system's dynamic reaction needed a brief time till the current began following its reference.
All the experimental results are generally in agreement with the simulated ones and the theoretical analyses presented in the previous sections.These simulation and experiment results verify the theoretical analysis precision and confirm that the proposed integrated DTLCL filter keeps the advantages of the discrete SPRLCL and LCL filters and overcomes their disadvantages.The results show that the presented filter performs similarly to the discrete SPRLCL filter, the proposed parameter design approach is effective, and the proposed parameter robustness analysis technique is accurate.Furthermore, the integrated DTLCL filter has flexibility and performance under different working conditions.

Conclusion
A magnetic integrated double-trap filter, referred to as DTLCL, is proposed in this paper for traction rectifiers to lessen the inductors' size and weight because the space on high-speed trains is highly constrained while suppressing the dominating current switching harmonics.Based on traditional LCL filters, a tiny capacitor placed in parallel with the grid-side inductor could be used for constructing an LC-trap.Another LC-trap could be created by introducing the coupling inductance into the filter capacitor branch via the magnetic coupling of the inverter-side and grid-side windings.It is possible to tune these two LC traps to specific harmonic frequencies  using a stepwise design method.The proposed filter can achieve the same harmonic suppression performance as the discrete double-trap filter, such as the SPRLCL filter, and save two magnetic cores of two trap inductors.
Furthermore, the presented filter has a magnetic core structure like the integrated LCL one but performs better in harmonic suppression.In addition, the resonance frequency is set over the Nyquist frequency, which equals half the sampling frequency, for using this design.The presented double-trap filter has been provided with a detailed step-by-step design method to facilitate the parameter choices.The developed filter could also withstand the grid impedance changes.After Simulink simulations and HIL experimental models were completed, the verification results were provided to demonstrate that the integrated DTLCL filter has the following advantages: 1.It has fewer discrete passive components than the discrete DTLCL and LCL filters.

Figure 1 .
Figure 1.Traction grid configuration of the power supply substation with EMU.

Figure 3 .
Figure 3. Proposed magnetic integration of DTLCL filter.(a) Core configuration of the integrated inductors and (b) simplified magnetic circuit.

Figure 4 .
Figure 4. Circuit configuration of an integrated DTLCL filter.

Figure 6 .
Figure 6.Bode diagrams for traction converters with integrated DTLCL and discrete SPRLCL, LCL, and L filters.

Figure 8 .
Figure 8. Simulated results using the integrated DTLCL filter.(a) i i , i g , v gg , and V dc waveforms, (b) i g and i i spectra.

Figure 9 .
Figure 9. Simulated results using the discrete SPRLCL filter.(a) i i , i g , v gg , and V dc waveforms, (b) i g and i i spectra.

Figure 10 .
Figure 10.Simulated results using the discrete LCL filter.(a) i i , i g , v gg , and V dc waveforms, (b) i g and i i spectra.

Figure 11 .Figure 12 .
Figure 11.Simulated results using the discrete L filter.(a) i g , v gg , and V dc waveforms, (b) i g spectrum.

Figure 16 .
Figure 16.Experimental waveforms and grid-side current spectrum using the integrated DTLCL filter.

Figure 17 .
Figure 17.Experimental waveforms and grid-side current spectrum using the discrete SPRLCL filter.

Figure 18 .
Figure18.Experimental waveforms and grid-side current spectrum using the discrete LCL filter.

Figure 19 .
Figure 19.Experimental waveforms and grid-side current spectrum using the traditional L filter.

Figure 20 .
Figure 20.Experimental waveforms using the integrated DTLCL filter with 2.5Ω step-up variation to R dc .

2 .
Compared to other conventional passive filters, it effectively suppresses harmonics.3. Flexibility in filter design and effectiveness of magnetic integration.4. It has durability and stability to transient and dynamic occurrences.

.
Single-phase H-bridge PWM traction inverter with an integrated DTLCL filter.current passing the C f .Moreover, v pcc denotes the voltage at the point of common coupling.At this point, the inverter is tied to the grid.

Table 2 .
Parameter values for the EMUs inverter.